I continued reading the Starlink patent US12003350 and summarized the information related to the use of the Unique Word (UW). The patent was filed in early 2021, so readers should consider its timeliness accordingly.
The UW is used differently on different communication links.
Satellite–Terminal Link
Uplink: When multiple terminals access the same satellite, each terminal is assigned a different UW. The UW is generated by a 7-stage LFSR-based PN generator, driven by the Channel ID.
Downlink: When multiple satellites cover the same geographic area, for example to improve reliability or avoid signal blockage, each satellite is assigned a different UW.
Satellite–Gateway Link
Communication between a satellite and a gateway station is always point-to-point. There is no scenario in which multiple satellites communicate with the same gateway simultaneously, or multiple gateways communicate with the same satellite simultaneously.
However, this link uses two Ka-band polarizations, LHCP and RHCP, and a different UW is assigned to each polarization.